Solve for $x$ and $y$ using substitution. ${-6x+6y = -12}$ ${y = 5x-6}$
Solution: Since $y$ has already been solved for, substitute $5x-6$ for $y$ in the first equation. ${-6x + 6}{(5x-6)}{= -12}$ Simplify and solve for $x$ $-6x+30x - 36 = -12$ $24x-36 = -12$ $24x-36{+36} = -12{+36}$ $24x = 24$ $\dfrac{24x}{{24}} = \dfrac{24}{{24}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = 5x-6}\thinspace$ to find $y$ ${y = 5}{(1)}{ - 6}$ $y = 5 - 6$ $y = -1$ You can also plug ${x = 1}$ into $\thinspace {-6x+6y = -12}\thinspace$ and get the same answer for $y$ : ${-6}{(1)}{ + 6y = -12}$ ${y = -1}$